Israeli warplanes hit Islamic Jihad targets in central and southern Gaza early on Monday after Palestinian rocket fire struck Israel, sources from both sides of the conflict said.

The raids came just hours after militants fired five rockets at southern Israel, two of which were intercepted by the Iron Dome anti-missile system, the military said.

The air force "targeted terrorist infrastructure including two weapon storage facilities in the central Gaza Strip and a rocket launch site in the southern Gaza Strip," a statement said.

Palestinian witnesses said the air raids hit uninhabited sites belonging to the radical Islamic Jihad movement, which is currently feuding with Gaza's Hamas rulers.

Avital Leibovich, a military spokeswoman, blamed the attack on Islamic Jihad, writing on Twitter that it had "fired five rockets into Israel" noting that the overnight raids had struck sites which "belonged to the Palestinian Islamic Jihad."

"When Hamas wants, they know how to keep order in the Strip," a military statement said. "We believe this was an isolated incident, but will continue to follow."

No group has claimed responsibility for the rocket fire but military officials quoted by the radio also pointed to Islamic Jihad.

The sudden rocket fire came just hours after Islamic Jihad publicly severed all contacts with Hamas after one of its military commanders died after being shot by Hamas policemen, a Jihad official told AFP.

Islamic Jihad is the second largest armed group in Gaza after Hamas and claims to have 8,000 fighters in its military wing.

As the ruling authority, Hamas is responsible for ensuring that militant groups respect the terms of an Egyptian-brokered truce which ended a major eight-day confrontation with Israel in November.

The rockets fired at Israel were most likely "Islamic Jihad's way of settling the score with Hamas," wrote Amos Harel, military correspondent for daily newspaper Haaretz.

But neither Hamas nor Israel have an interest in escalating the situation, he continued, and therefore the Jewish state "restricted its responses to an aerial attack on a weapons cache, and an Islamic Jihad command centre, while also temporarily closing border crossings."

In response to the rockets, the defence ministry ordered closure of the two terminals to Israel - Erez and the Kerem Shalom commercial crossing - with the army saying both would be closed until further notice.

"Our policy is to strike at those who try to harm us," said Prime Minister Benjamin Netanyahu on Monday, warning Israel would answer both "near threats and distant threats."

Earlier, Avigdor Lieberman who heads the parliament's foreign and defence committee told public radio that Israel should consider reoccupying Gaza and "cleansing" it.

"In another two years, Hamas will have thousands of rockets that could reach Tel Aviv and beyond," said the MP who is a senior member of the ruling rightwing Likud-Beitenu. "We will find ourselves in a reality that they have all kinds of aircraft and rockets, Hamas is not losing time."

"Since Hamas has no intention to recognise Israel or coexist in peace or accept the Jewish presence in Israel, there will be no alternative and eventually Israel will have to seriously consider the possibility of occupying all of the Strip and carrying out a serious cleansing," he said.

Israel seized Gaza from Egypt in 1967, but unilaterally withdrew all its troops and settlers in 2005.

Hamas prime minister Ismail Haniya rejected the remarks.

"We are not afraid of these threats, but at the same time our duty is to protect our people and preserve the internal situation," he said, referring to the ceasefire deal inked in November.